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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nakai conjecture ： ウィキペディア英語版 Nakai conjecture In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961.〔.〕 It states that if ''V'' is a complex algebraic variety, such that its ring of differential operators is generated by the derivations it contains, then ''V'' is a smooth variety. The converse statement, that smooth algebraic varieties have rings of differential operators that are generated by their derivations, is a result of Alexander Grothendieck.〔. Schreiner cites this converse to EGA 16.11.2.〕 The Nakai conjecture is known to be true for algebraic curves〔.〕 and Stanley-Reisner rings.〔.〕 A proof of the conjecture would also prove the Zariski–Lipman conjecture, for a complex variety ''V'' with coordinate ring ''R''. This conjecture states that if the derivations of ''R'' are a free module over ''R'', then ''V'' is smooth.〔.〕 ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nakai conjecture」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.